## Re: [Libmesh-users] Mixed derivative representation in libMesh

 Re: [Libmesh-users] Mixed derivative representation in libMesh From: Roy Stogner - 2006-07-29 08:54:52 ```On Fri, 28 Jul 2006, David Xu wrote: > I was wondering how to write down an equation containing mixed derivative in > libMesh's element matrix (Ke) building step? > > For exmaple, Uxx+Uyy+Uxy (U is 2nd order derivative) If you need mixed second derivatives of a shape function, take a look at example 15, which solves a biharmonic equation by a direct Galerkin method which computes laplacians at each quadrature point. If you need derivatives of your solution, take a look at how solutions and their derivatives are accumulated in example 13 - you'd do the same thing but with Tensor/RealTensor classes instead of Gradient/RealGradient. --- Roy ```

 [Libmesh-users] Mixed derivative representation in libMesh From: David Xu - 2006-07-28 22:17:09 Attachments: Message as HTML ```Hi All, I was wondering how to write down an equation containing mixed derivative in libMesh's element matrix (Ke) building step? For exmaple, Uxx+Uyy+Uxy (U is 2nd order derivative) Thanks! David ```
 Re: [Libmesh-users] Mixed derivative representation in libMesh From: Roy Stogner - 2006-07-29 08:54:52 ```On Fri, 28 Jul 2006, David Xu wrote: > I was wondering how to write down an equation containing mixed derivative in > libMesh's element matrix (Ke) building step? > > For exmaple, Uxx+Uyy+Uxy (U is 2nd order derivative) If you need mixed second derivatives of a shape function, take a look at example 15, which solves a biharmonic equation by a direct Galerkin method which computes laplacians at each quadrature point. If you need derivatives of your solution, take a look at how solutions and their derivatives are accumulated in example 13 - you'd do the same thing but with Tensor/RealTensor classes instead of Gradient/RealGradient. --- Roy ```